A five-card poker hand is dealt from a standard deck of cards.
So the denominator of each probabilities will be:
(52 cards, choose 5) = 52C5 = 2598960
Find the probability that:
a. The hand contains exactly 3 hearts and exactly 2 spades
(13 hearts, choose 3)ื(13 spades, choose 2) = (13C3)ื(13C2) = 22308
Probability = 22308/2598960 = 143/16660
b. The hand contains 2 of one kind and 3 of another kind
(kind means the face value of the card. e.g. 3 or Q)
Probability = 3744/2598960 = 6/4165
c. The hand consists of at least 3 Kings.
Case 1: Hand contains exactly 3 Kings:
(4 Kings, choose 3)ื(48 non-Kings, choose 1) = (4C3)ื(48C1) = 4ื48 = 192
Case 2: Hand contains all 4 Kings:
(4 Kings, choose 4) = 4C4 = 1
Total for Case 1 and Case 2 = 192+1 = 193
Probability = 193/2598960
Edwin